Method and System For Error Correction in Flash Memory

ABSTRACT

A controller is described for a multi-level, solid state, non-volatile memory array having memory cells. The memory cells are configured to store data using a first number of digital levels. The controller is configured to encode multiple data bits to generate multiple encoded data bits, convert the multiple encoded data bits into multiple data symbols, and send the multiple data symbols for storage in a memory cell of the multi-level, solid state, non-volatile memory array. The controller is further configured to generate an output signal, using a second number of digital levels, based on data associated with the multiple data symbols stored in the memory cell. The second number of digital levels is greater than the first number of digital levels used to store the multiple data symbols in the memory cell. The controller is further configured to output multiple output data symbols based on the output signal.

CROSS-REFERENCES TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.12/946,520, filed on Nov. 15, 2010, which is a continuation of U.S.patent application Ser. No. 11/598,117 (now U.S. Pat. No. 7,844,879),filed on Nov. 8, 2006, which claims the benefit of U.S. ProvisionalApplication No. 60/760,622, filed on Jan. 20, 2006, U.S. ProvisionalApplication No. 60/761,888, filed on Jan. 25, 2006; and U.S. ProvisionalApplication No. 60/771,621, filed on Feb. 8, 2006. The entiredisclosures of the above referenced applications are incorporated hereinby reference.

This application is also related to U.S. patent application Ser. No.11/598,178 (Attorney Docket No. MP0916), now U.S. Pat. No. 8,055,979,entitled “Flash Memory with Coding and Signal Processing,” filed on Nov.8, 2006, the entire application is incorporated herein by reference.

BACKGROUND OF THE INVENTION

The present invention relates generally to integrated circuits. Moreparticularly, the invention relates to a method and system forperforming error correction in multi-level solid state non-volatilememories.

Solid state non-volatile memories, such as flash EEPROM memories, areused in a variety of electronics applications. Flash memories are usedin a number of memory card formats, such as CompactFlash (CF),MultiMediaCard (MMC) and Secure Digital (SD). Electronic systems inwhich such cards are used include personal and notebook computers,hand-held computing devices, cameras, MP3 audio players, and the like.Flash EEPROM memories are also utilized as bulk mass storage in manyhost systems.

Conventional solid state memories store information as a series ofbinary digits or “bits,” which can take on one of two different values(0 or 1). Bits are grouped together to represent larger numbers.

As with most solid state non-volatile memory devices, flash EEPROMs aresusceptible to defects and failures. Errors result from several factorsincluding the gradual shifting of the threshold level of the memorystates as a result of ambient conditions and stress from normaloperations of the memory device including program, erase, and readoperations. In order to prevent errors during operation, errorcorrection code (ECC) techniques are utilized in flash memory devices.Typically, a controller generates redundant bits (parity bits) that areappended to the end of data sectors during program operations. Forexample, a 512 byte data sector may have 16 bytes of ECC data appended,resulting in a 528 byte page. During read operations, the redundant dataincluded in the 16 bytes of ECC data is utilized to detect and correcterrors in the data read out from the flash memory.

For a conventional memory, the maximum storage density is determined bythe size of the individual storage elements and the number of storageelements that can be integrated onto a single integrated circuit chip.Typically, increases in memory density have been provided by shrinkingthe linewidth of the process geometry used to fabricate the memorycells.

Another technique used to increase solid state non-volatile memorydensity is storing more than one bit per memory cell, also referred toas a multi-level memory cell. Rather than sensing whether or not chargeis stored in a given memory cell (i.e., a binary cell), multi-levelmemories utilize a sense amplifier that senses the amount of chargestored in a capacitive storage cell. By quantizing information intounits greater than binary, e.g., 4-level (2 bits/cell), 8-level (3bits/cell), 16-level (4 bits/cell) units, and the like, and storingthese multi-level units, the memory density can be increased. As anexample, a cell may be programmed to produce four distinct thresholdlevels, which results in four distinct read-back levels. With a fourlevel signal available per cell, two data bits can be encoded into eachsolid state non-volatile memory cell. Multi-level memories enable themanufacturing of higher density memories without increasing the numberof memory cells since each memory cell can store more than a single bit.Merely by way of example, for a memory cell capable of storing 2bits/cell, there may be three programmed states and an erased state.FIG. 1 is a simplified probability distribution function (PDF) as afunction of voltage for a solid state non-volatile memory cell having a4-level quantization. In the memory cell illustrated in FIG. 1, fourprogrammed states are utilized. As illustrated, in some solid statenon-volatile memories, the PDF of programming characteristics has awider distribution at lower voltage levels.

However, increasing the number of quantization levels in a cell resultsin a reduction in the voltage difference between adjacent levels. Inmulti-level encoding systems, this reduction is sometimes referred to asreduced signal distance (reduced D_(min)). Reduced signal distance mayimpact non-volatile memory performance in both write (program) as wellas read operations. During programming, it is more difficult to transfermultiple discrete units of charge to a capacitive cell than it is simplyto fully charge or fully discharge the cell. Thus, uncertainty in theamount of charge transferred to a given cell may result in a levelshift, resulting in a “program disturb” in which the wrong level isstored in the cell. During reading, “read disturbs” occur when thedistribution of one signal level overlaps the distribution of anadjacent signal level. Because the signal distance is reduced, theincrease in the number of discrete values stored in the cell reduces thenoise margin of the cell as compared to a binary storage cell, makingthe storage element more prone to erroneous readout. Read disturbs aremore common for low-level signals, which are characterized by largernoise distributions as shown in FIG. 1.

The reduction in voltage separation between adjacent levels in amulti-level solid state non-volatile memory may lead to an increase inthe number of errors in comparison with conventional solid statenon-volatile memory cells. Thus, it would be desirable to provideimproved methods and techniques for operating solid state non-volatilememory with multi-level cells.

SUMMARY OF THE INVENTION

According to an embodiment of the present invention, a solid statenon-volatile memory unit is provided. The memory unit includes amulti-level solid state non-volatile memory array adapted to store datacharacterized by a first number of digital levels. The memory unit alsoincludes an analog-to-digital converter. The analog-to-digital converteris adapted to receive data from the multi-level solid state non-volatilememory array. The analog-to-digital converter is also adapted to outputa digital signal characterized by a second number of digital levelsgreater than the first number of digital levels.

According to another embodiment of the present invention, a method ofoperating a solid state non-volatile memory unit is provided. The methodincludes encoding a first data and storing the encoded first data in amulti-level solid state non-volatile memory array. The stored encodedfirst data is characterized by a first number of digital levels. Themethod also includes retrieving the first encoded data from the memoryarray and digitizing the retrieved data to a number of digital levelsgreater than the number of digital levels associated with themulti-level solid state non-volatile memory array.

According to an alternative embodiment of the present invention, acontroller for a multi-level solid state non-volatile memory arraycharacterized by a first number of digital levels is provided. Thecontroller includes a first encoder adapted to receive a series of databits and provide a series of encoded data bits. The controller alsoincludes a mapper adapted to convert the series of encoded data bitsinto a series of data symbols for storage in the multi-level solid statenon-volatile memory array. The controller further includes a firstdecoder adapted to receive a series of voltage signals from themulti-level solid state non-volatile memory array and generate a seriesof output data symbols characterized by a second number of digitallevels greater than the first number of digital levels.

According to yet another embodiment of the present invention, a methodof operating a controller for a multi-level solid state non-volatilememory array characterized by a first number of digital levels isprovided. The method includes encoding a first series of data bits toprovide a series of encoded data bits and converting the series ofencoded data bits into a series of data symbols. The method alsoincludes storing the series of data symbols in the multi-level solidstate non-volatile memory array and retrieving the series of datasymbols. The method further includes decoding the series of data symbolsto provide a series of output data symbols characterized by a secondnumber of digital levels greater than the first number of digitallevels.

According to a particular embodiment of the present invention, a solidstate non-volatile memory unit is provided. The memory unit includesmeans for encoding a first data and means for storing the encoded firstdata in a multi-level solid state non-volatile memory array. The storedencoded first data is characterized by a first number of digital levels.The memory unit also includes means for retrieving the first encodeddata from the memory array and means for digitizing the retrieved datato a number of digital levels greater than the number of digital levelsassociated with the multi-level solid state non-volatile memory array.

According to another particular embodiment of the present invention, acontroller for a multi-level solid state non-volatile memory arraycharacterized by a first number of digital levels is provided. Thecontroller includes means for encoding a first series of data bits toprovide a series of encoded data bits and means for converting theseries of encoded data bits into a series of data symbols. Thecontroller also includes means for storing the series of data symbols inthe multi-level solid state non-volatile memory array and means forretrieving the series of data symbols. The controller further includesmeans for decoding the series of data symbols to provide a series ofoutput data symbols characterized by a second number of digital levelsgreater than the first number of digital levels.

Still other embodiments of the present invention may be implemented incode, for example, by a digital signal processor (DSP). One suchembodiment includes code for encoding a first data and means for storingthe encoded first data in a multi-level solid state non-volatile memoryarray. The stored encoded first data is characterized by a first numberof digital levels. The embodiment also includes code for retrieving thefirst encoded data from the memory array and code for digitizing theretrieved data to a number of digital levels greater than the number ofdigital levels associated with the multi-level solid state non-volatilememory array.

In another embodiment implemented in code, for example, by a DSP, codefor controlling a multi-level solid state non-volatile memory arraycharacterized by a first number of digital levels is provided. Theembodiment includes code for encoding a first series of data bits toprovide a series of encoded data bits and code for converting the seriesof encoded data bits into a series of data symbols. The embodiment alsoincludes code for storing the series of data symbols in the multi-levelsolid state non-volatile memory array and code for retrieving the seriesof data symbols. The embodiment further includes code for decoding theseries of data symbols to provide a series of output data symbolscharacterized by a second number of digital levels greater than thefirst number of digital levels.

Many benefits are achieved by way of the present invention overconventional techniques. For example, embodiments of the presentinvention provide solid state non-volatile memory systems with increasedstorage density. Moreover, some embodiments improve the reliability ofdata read from solid state non-volatile memories. Depending upon theembodiment, one or more of these benefits, as well as other benefits,may be achieved. These and other benefits will be described in moredetail throughout the present specification and more particularly belowin conjunction with the following drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a simplified probability distribution function as a functionof voltage for a solid state non-volatile memory cell having a 4-levelquantization;

FIG. 2A is a constellation diagram for an uncoded one bit PAM scheme;

FIG. 2B is a constellation diagram for a two-bit data modulated using aPAM scheme having an average power of 1;

FIG. 2C is a constellation diagram for a two-bit data modulated using aPAM scheme having a peak limit of ±1 for use in a solid statenon-volatile memory cell;

FIG. 3A is a simplified block diagram of an exemplary solid statenon-volatile memory unit with error correction code according to anembodiment of the present invention;

FIG. 3B is a simplified block diagram of a solid state non-volatilememory unit incorporating an analog-to-digital converter according to anembodiment of the present invention;

FIG. 4 is a simplified block diagram of a solid state non-volatilememory unit with error correction according to another embodiment of thepresent invention;

FIG. 5 shows a word error rate (WER) of a memory unit, in accordancewith one exemplary embodiment of the present invention, as compared to aconventional uncoded system;

FIG. 6 shows various blocks of an exemplary rate ½ convolutional encoderaccording to an embodiment of the present invention;

FIG. 7 shows an example of 2-D set partitioning according to anembodiment of the present invention;

FIG. 8 is a simplified block diagram of a conventional TCM encoder;

FIG. 9 illustrates an example of combining set-partitioning withiterative code according to an embodiment of the present invention;

FIG. 10A is a simplified illustration of a two-level system thatincludes an inner code and an outer code according to an embodiment ofthe present invention;

FIG. 10B is a simplified block diagram of a two-level encoding channelaccording to another exemplary embodiment of the present invention;

FIGS. 11A-11C show a number of exemplary sector and codeword sizes, inaccordance with the present invention;

FIG. 12 illustrates an exemplary 3-way interleaved cell according to anembodiment of the present invention;

FIG. 13A is a simplified schematic diagram of an interleaving techniqueprovided according to an exemplary embodiment of the present invention;

FIG. 13B is a plot of SER as a function of SNR for an interleaved systemas illustrated in FIG. 13A; and

FIGS. 14A-14H show various devices in which the present invention may beembodied.

DETAILED DESCRIPTION OF SPECIFIC EMBODIMENTS

FIG. 2A is a constellation diagram for an uncoded one bit PAM (pulseamplitude modulation) scheme according to which, information is storedas either a 0 (−1 volts) or a 1 (+1 volts). FIG. 2B is a constellationdiagram for a two-bit data modulated using a PAM scheme having anaverage power of 1. The four states defined by the two bits, namelystates (00, 01, 10, and 11) are mapped to one of four possible levels,for example, −3/√5 volts, −1/√5 volts, +1/√5 volts, and +3/√5 volts.Given these voltages, both the 2-points PAM (2-PAM) and the 4-points PAM(4-PAM) with ½ code rate provide a 1 bit/cell spectral efficiency andare characterized by equal power. For the modulation scheme illustratedby FIG. 2B, the 4-state code with Gray mapping reduces bit error rateover the 4-state natural mapping.

In solid state non-volatile memory devices, the maximum voltage appliedat the floating gate limits the maximum voltage available for mapping ofmulti-level symbols. This voltage limitation results in a peakconstraint on the constellation values of the applied modulation andencoding scheme. Thus, for a solid state non-volatile memory device, theconstellation points must account for this limitation. The maximumvoltage constraint characteristic of solid state non-volatile memorysystems constrasts with other channels in which additional powerincreases are available. Accordingly, embodiments of the presentinvention utilize modulation and encoding schemes for multi-levelnon-volatile solid state memories designed to be operable in spite ofsuch constraints.

FIG. 2C is a constellation diagram for a two-bit data modulated using aPAM scheme having a peak value limited to ±1 for use in a solid statenon-volatile memory cell. Symbol 00 is mapped to a signal amplitude of−1 volts and symbol 10 is mapped to a signal amplitude of +1 volts,which in this example, correspond to the maximum voltages stored by agiven solid state non-volatile memory cell. Applying power scaling toaccount for the maximum allowable voltage across the non-volatile solidstate memory cells, it is seen that the squared free distance is reducedby a factor of 5/9, resulting in a 0 dB coding gain over an uncoded2-PAM system.

As the number of levels increases, the signal to noise ratio (SNR)decreases. However, the slope of the SNR decrease is not the same forthese two systems. Referring to FIGS. 2B and 2C, the SNR is related tothe minimum distance between the nearest neighbors in the constellationmap. Consequently, voltage constraints in solid state non-volatilememory devices reduce the available minimum distance and the SNR.Therefore, for a given number of levels, memory systems generally have alower SNR compared to other known systems. As a result of thesedifferences, the encoding and modulation techniques, in accordance withvarious embodiments of the present invention, are adapted to theenvironment characteristic of solid state non-volatile memories.

Assuming equal energy constellations, for an uncoded system, the errorprobability (P_(uncoded)) is upper bounded by:

$\begin{matrix}{{P_{uncoded} \leq {A_{\min}{Q( \sqrt{\frac{d_{\min}^{2}}{2\; N_{0}}} )}} \approx {\frac{A_{\min}}{2}{\exp ( \frac{- d_{\min}^{2}}{4\; N_{0}} )}}},} & (1)\end{matrix}$

where A_(min) is the number of nearest neighbors, d_(min) ² is theminimum distance squared between two points in a constellation, and Q(x)is the complementary error function (co-error function).

For a coded system:

$\begin{matrix}{{P_{coded} \leq {A_{dfree}{Q( \sqrt{\frac{d_{dfree}^{2}}{2\; N_{0}}} )}} \approx {\frac{A_{dfree}}{2}{\exp( \frac{- d_{dfree}^{2}}{4\; N_{0}} )}}},} & (2)\end{matrix}$

where d_(free) is the minimum distance.

The asymptotic coding gain is defined by:

$\begin{matrix}{\gamma = {\frac{d_{dfree}^{2}}{d_{\min}^{2}}.}} & (3)\end{matrix}$

For the coded system, the minimum distance d_(free) is generallyincreased in comparison to the uncoded system, resulting in anasymptotic coding gain greater than one. However, the number of nearestneighbors also increases so the real coding gain is somewhat reduced.

FIG. 3A is a simplified block diagram of an exemplary solid statenon-volatile memory unit 300 with an ECC according to an embodiment ofthe present invention. User data to be written into the multi-levelmemory cells of multi-level solid state non-volatile memory 314 are ECCencoded by encoder 310 to add redundant symbols. The encoded data ispassed to modulator 312 for channel encoding. According to embodimentsof the present invention, any one of a number of encoding and modulationtechniques may be used.

Multi-level solid state non-volatile memory 314 receives encoded andmodulated data from modulator 312. Multi-level solid state non-volatilememory 314 may be a flash EEPROM, or the like. Generally, a multi-levelflash memory includes one or more flash memory cell arrays and read andwrite (program) circuitry. In addition to a multi-level flash memory,there are other types of solid state non-volatile memory technologiesthat are included within the scope of the present invention. Floatinggate memory cells such as flash memories are discussed herein merely byway of example. Embodiments of the present invention as describedthroughout the present specification also apply to other memorytechnologies other than floating gate technology with the appropriatemodifications. One of ordinary skill in the art would recognize manyvariations, modifications, and alternatives.

Data is read from multi-level solid state non-volatile memory 314 andpasses to demodulator 316 and decoder 318. The demodulator inembodiments of the present invention includes signal processing logicadapted to extract soft information related to the data stored in themulti-level solid state non-volatile memory 314. In conventional binarynon-volatile memory systems, a threshold detector is utilized todetermine if a voltage value associated with a particular cell is lessthan or greater than a given threshold value. This threshold-basedapproach is also utilized in multi-level memory systems, where thethreshold detection circuit merely utilizes a greater number ofthreshold values. Although some multi-level memory systems includecircuitry that tracks process or other variations and adjusts thethreshold values accordingly, these systems output a value from a numberof possible values that is equal to the number of levels in themulti-level system. Thus, for example, for a conventional four-levelnon-volatile memory, the sense amplifier will produce a data signalrepresenting one of the four levels.

In contrast with conventional multi-level memory systems, embodiments ofthe present invention utilize a demodulator that produces an outputhaving a number of possible values greater than the number of levelsprovided by the multi-level solid state non-volatile memory 314. Thisinformation is sometimes referred to as soft information since theoutput includes information in addition to the value stored in themulti-level memory. Merely by way of example, an analog-to-digital (A/D)converter or detector provided as part of or working in conjunction withdemodulator 316 provides an output signal with, for example, 32 possiblevalues in response to the values detected by a sense amplifier disposedin communication with, for example, a four-level memory. Embodiments ofthe present invention are not limited to using an output signal with 32levels, as other output signals, with, for example, 8, 16, or morelevels are included within the scope of the present invention. In someapplications, the soft information is passed to a soft informationdecoder (not shown) for processing. In embodiments of the presentinvention, the soft information provided by the demodulator 316 isutilized during signal processing operations to improve the reliabilitywith which data from the solid state non-volatile memory 314 is read.

In an embodiment of the present invention, encoder 310, modulator 312,demodulator 316, and decoder 318 are components of a controller incommunication with multi-level solid state non-volatile memory 314.Memory devices typically include one or more memory chips that aremounted on a card. Each of the memory chips may include an array ofmemory cells as well as integrated circuits performing such operationsas program, read, and erase. According to embodiments of the presentinvention, a controller circuit performing these operations may or maynot be disposed in the integrated circuits (IC) in which the memorychip(s) are also disposed. Controllers provided herein are not limitedto performing encoding/decoding and modulation/demodulation processes,but may also provide for other functionality such as wear leveling andinterfacing processes.

Embodiments of the present invention enable system designers to increasethe memory density of existing solid state non-volatile memories. Asdescribed more fully throughout the present specification, in comparisonwith conventional systems, increased levels of read and write errors arecorrected utilizing the techniques and methods provided herein. Thus,although attempting to utilize, for example, a four-level memory systemfor, for example, eight-level applications by introducing additionallevels may produce a greater number of errors during read operationsthan is otherwise acceptable under a given performance measure,techniques described herein may be utilized to correct such errorsduring the demodulation process and enable the use, for instance, of afour-level memory system in an eight-level application. Thus, inaccordance with the present invention, the memory density of existingsolid state non-volatile memory systems may be increased while stillusing some of the same components, including memory arrays, senseamplifiers, and the like.

FIG. 3B is a simplified block diagram of a solid state non-volatilememory unit 350 incorporating an A/D converter according to anembodiment of the present invention. As illustrated in FIG. 3B, anencoder 360 and a modulator 362 provide encoded and modulated data tothe multi-level non-volatile solid state memory 364. A/D converter 366receives signals from the multi-level non-volatile solid state memory364. The digital signal output by the A/D converter 366 is of higherresolution (characterized by more levels) than the number of levelsassociated with the multi-level non-volatile solid state memory 364.Merely by way of example, in a particular embodiment, the multi-levelnon-volatile solid state memory 364 is, for example, a four-levelmemory, providing storage for 2 bits in each cell. During a readoperation, the A/D converter 366 converts an analog signal associatedwith one or more cells of the memory 364 into one of, for example, 8,16, 32, or 64 levels depending on the particular application. Othernumbers of levels greater than four levels are used in otherembodiments. Signal processing algorithms resident in demodulator 368utilize the output of the A/D converter 366 to determine the likelihoodthat the cell contains data associated with one of the four levelsstored in the cell. One of ordinary skill in the art would recognizemany variations, modifications, and alternatives.

In conventional solid state memories, ECC techniques are utilized todetect and correct errors in data as the data is read out from thememory. Such ECC techniques simply operate on binary or multi-leveldigital data produced by a sense amplifier. On the other hand, inaccordance with the present invention, soft information produced andutilized by the demodulator 316 does not merely include the binary ormulti-level digital data, but additional information as well. Softinformation is typically represented by distributions that are useful inperforming signal processing techniques not generally applicable oncethe data has been reduced to threshold-based digital values equal innumber to the number of levels in the multi-level system.

Utilizing embodiments of the present invention, positive coding gain isachieved for multi-level solid state non-volatile memory systems incomparison to uncoded systems. Table 1 illustrates an exemplary codinggain from convolutional coded 2 bit/cell multi-level non-volatile memoryover an uncoded 1 bit/cell non-volatile memory as a function of thenumber of states of the code. As shown in the first row entry, for a4-state system (illustrated by FIGS. 2A-2C), the coding gain incomparison to an uncoded system is 0 dB. However, as the number ofstates is increased, the coding gain in comparison to an uncoded systemis positive.

TABLE 1 Number of States Coding Gain (dB) 4 0 8 0.46 16 0.87 32 1.50

Table 2 illustrates the coding gain for convolutional coded 3 bit/cellmulti-level non-volatile memory over uncoded 2 bit/cell multi-levelnon-volatile memory as a function of the number of states of the code.As shown for 1 bit/cell multi-level non-volatile memory with four ormore states, the coding gain in comparison to an uncoded system ispositive for systems with four or more states.

TABLE 2 Number of States Coding Gain (dB) 4 2.18 8 2.64 16 3.05 32 3.78

FIG. 4 is a simplified block diagram of a solid state non-volatilememory unit with error correction according to another embodiment of thepresent invention. As illustrated in FIG. 4, an outer encoder 410provides encoded data to an inner encoder 412. As an example, outerencoder 410 may be a Reed-Solomon encoder and inner encoder may be anLDPC encoder. These encoding techniques are used merely as examples andare not intended to limit the scope of the present invention. One ofordinary skill in the art would recognize many variations,modifications, and alternatives. Modulator 414 receives encoded datafrom inner encoder 412 and modulates the data prior to storage inmulti-level solid state non-volatile memory 416 during a programoperation. During a read operation, the data stored in the multi-levelsolid state non-volatile memory 416 is retrieved and provided todemodulator 418, inner decoder 420, and outer decoder 422.

Any number of Error Correcting Codes (ECCs) including Forward ErrorCorrection (FEC) codes may be used according to embodiments of thepresent invention to improve the bit error rate (BER) performance ofpower-limited and/or bandwidth-limited channels by adding structuredredundancy to the transmitted data. For example, block codes may be usedto encode a block of data for channels with additive burst noise (randommulti-bit errors). It is understood that the present invention isapplicable to both systematic encoders that do not manipulate the userdata prior to encoding and storage, as well as to non-systematicencoders.

Any one of a number of different linear block codes including, forexample, binary codes such as Hamming code, BCH code, Reed-Muller codeand Array Code, and non-binary codes such as Reed-Solomon (RS) code maybe used. Choice of block size depends on SNR and the code used. Forexample, assume that the voltage levels are increased from 4 to 8 percell, and that each three cells are grouped together to form a 9-bitsymbol. Applying a (511, 451) Reed-Solomon code, based on GF(2⁹), thecodeword length is 511*9=4599 bits, and the code rate is451/511^(˜)=0.883. Therefore, the storage capacity for the coded systemis 3*451/511^(˜)=2.6 bits/cell, which represents a 32% capacity increaseover uncoded 4-level system. The word error rate (WER) of such a codedsystem is compared to a 4-level uncoded system in FIG. 5. It can be seenat WER<10⁻⁸, the RS coded system outperforms the uncoded system.Therefore, with the above RS code, better reliability and highercapacity is achieved.

In accordance with other exemplary embodiments of the present invention,for example, when the noise is independent from symbol to symbol,convolutional codes are used to encode the data. Convolutional codesintroduce correlation into coded data and thus increase the minimumdistance at the decoder. Convolutional codes are applied toserially-transmitted data stored in or read from solid statenon-volatile memories, which are subject to Gaussian noise.Convolutional codes are progressive codes. At any point in time, theoutput of a convolutional encoder may depend upon both the past andpresent input values. Thus, convolutional codes are generally directedto correcting errors that span an ordered progression of data values.Accordingly, such codes may be used in multi-level solid statenon-volatile memories that store and read out data in the form of anordered, progressive stream (i.e., a data stream).

The decoder receives either hard decision inputs or multi-levelquantized inputs. Soft inputs are known to cause fewer errors at thedetector. FIG. 6 shows various blocks of an exemplary rate ½convolutional encoder 600. Output C2 generated by modulo-2 adder 610 isdefined by shift registers 602, 606 and input U. For example, if thevoltage levels are increased from four to eight, applying a rate ¾convolutional code to get 3*¾=2.25 bits/cell, results in a 10% increasein storage capacity. To achieve the same error rate as uncoded 4-levelsystem, the free distance of the convolutional code must be greater than(7/3)²=5.44. A ¾ convolutional encoder with six memory units wouldrequire a Viterbi decoder with 2⁶=64 states.

Trellis coded modulation (TCM) combines convolutional code with setpartitioning to achieve high code rate, high coding gain, and lowdecoding complexity. A set of constellation points can be partitioned toa smaller subset, where points in each subset are separated further thanin the original constellation. FIG. 7 shows an example of 2-D setpartitioning where dots, “∘”, represent one subset, and crosses, “x”,represent the other. If the minimum distance between the originalconstellation points is d, then the minimum distance between points ineach subset is √{square root over (2)}d. In systems with additive whiteGaussian Noise (AWGN) channels, such as flash memory systems read pathchannels, the parameter governing the performance of the system is notthe free Hamming distance of the convolutional code, but rather the freeEuclidean distance between the transmitted signal sequences.Accordingly, the optimization of the TCM design is based on theEuclidean distances rather than the Hamming distances.

An example of TCM is shown in FIG. 8. Input bits are separated into twogroups—a first group with k_(l) bits, going through a ratek_(l)/(k_(l)+l) encoder 802 to select subsets; a second group with k-k₁bits, which select constellation points, using constellation mapper 804,within each subset. Below is a description of an exemplary increase incapacity from 2 bits/cell to 2.5 bits/cell. Assume that there are 8voltage levels and that each two adjacent cells is combined to form a 64QAM constellation. The 64 QAM is partitioned into 4 cosets. Distancebetween any two points in each coset is 8*d0. Assume a rate ¾convolutional code is used to select a coset, and two uncoded bits areused to select a point within any given coset. The overall code ratewould thus become ⅚, leading to 2.5 bits/cell. The overall coding gainis 0.43 dB. Therefore, such a TCM coded system has a better performancethan the uncoded 4 level system while increasing the storage capacity by25%.

Some codes based on random construction may be effectively decoded byiterative detection methods. These codes include Turbo codes, i.e.,serially concatenated convolutional codes, or parallel concatenatedconvolutional codes, low-density parity-check (LDPC) codes, TurboProduct code, and their variations.

Coding gain of TCM comes from two areas—set partitioning to increase thedistance between constellation points within each subset, andconvolutional code to achieve high Euclidean distance between differentsubsets, the latter of which can also be achieved if other high gaincodes are substituted for convolutional code. An example of combiningset-partitioning with iterative code is shown in FIG. 9. Assume a 16-PAMsystem is partitioned into 4 subsets. Then the minimum distance betweenpoints in each subset is 4d₀, hence providing a 12 dB gain compared touncoded system. However, between different subsets, the minimum distanceremains at d₀. Since the selection of subset depends on LDPC coded bitssupplied by LDPC encoder 902, then the overall system has an approximategain of 12 dB if an LDPC code having a gain of 12 dB is used. Ingeneral, the overall system gain is the minimum of the set-partitioninggain and the iterative coding gain. LDPC encoder 902 shown in FIG. 9 isrequired to operate on a whole codeword defined by the iterative codeblock size. In addition to iterative codes, other high gain codesincluding RS code and BCH code may be used to code a portion of theinput for subset selection.

In accordance with some embodiments, to further improve coding gain,multi-level coding may be used. A two-level encoding that includes aninner encoder and an outer encoder is shown in FIG. 10A. In oneexemplary embodiment, outer code encoder 1002 may be a RS encoder, andinner code encoder 1004 may be a TCM encoder. Bursty errors caused byTCM decoder 1006 are corrected by RS decoder 1008.

In another exemplary embodiment, inner encoder 1004 is adapted toperform iterative codes, such as LDPC codes or Turbo codes, and outerencoder 1002 is adapted to perform RS code. Iterative codes may bebinary codes or symbol-based codes. Each symbol may contain multiplebits. Iterative codes may be decoded using a soft-input soft-output(SISO) decoder, while RS codes may be decoded using either a SISO or ahard-decision decoder. The outer RS decoder 1008 may iterate with innerdecoder 1006 to exchange soft information. Such iteration would improvethe quality of soft information and thereby decrease the number of biterrors after each iteration.

The descriptions of the various embodiments provided herein are providedmerely by way of example, and are not intended to limit the scope of thepresent invention. Various other coding techniques, interleavingtechniques, modulation techniques, demodulation techniques, decodingtechniques, mapping techniques, and the like are included within thescope of the present invention.

FIG. 10B is a simplified block diagram of a two-level encoding 1020, inaccordance with another exemplary embodiment of the present invention.The outer encoder 1022 is a Reed-Solomon encoder with a correction powert. Inner encoder 1030 includes a TCM 1024 having a code rate ¾, and a16-PAM constellation mapper 1026 having a spacing between any two pointsof 2/15. For calculations performed for the encoding channel shown inFIG. 10B, convolutional encoders with polynomials of order 3, 4, and 5are utilized. It is understood that although the exemplary embodimentshown in FIG. 10B includes a Reed-Solomon encoder 1022, a TCM 1024, anda 16-PAM constellation mapper 1026, other embodiments of the presentinvention may include other encoders, modulators, and mappers. Moreover,for all the exemplary embodiments described herein and shown in thedrawings, modulators including multi-dimensional ones such as thoseproposed by Wei, “Trellis-Coded Modulation with MultidimensionalConstellations” IEEE Transactions on Information Theory, Volume IT-33,No. 4, (July 1987), pgs. 483-501; and multilevel codes such as thoseproposed by Imai and Hirakawa, “A New Multilevel Coding Method UsingError-Correcting Codes” IEEE Transactions on Information Theory, VolumeIT-23, No. 3, (May 1977) pgs. 371-377, any combinations thereof, and thelike may be used.

Referring to FIG. 10B, approximately 2 kbits (2048 bits) are representedby 228 9-bit symbols. Merely by way of example, the 9-bit symbols areformed by combining three adjacent 8-level cells. The 228 9-bit symbolsare supplemented with 2t symbols by the Reed-Solomon encoder 1022 toprovide 230 symbols that are input to the inner encoder 1030. In anexemplary embodiment, user data represented by the 228 9-bit symbols iswritten into a portion of a memory array characterized by a width equalto thirty 3-bit cells. After the user data is written into the memoryarray in a serial manner, three adjacent 3-bit cells are grouped to forma 9-bit symbol. The ten columns of such 9-bit symbols are then appendedwith column parity values provided, for example, by the RS encoder 1022.The number of appended parity values will depend, in part, on thecorrection power selected for the RS encoder 1022. TCM encoding isperformed on each 3-bit cell to provide encoded 4-bit symbols, which aresubsequently provided to the 16-PAM constellation mapper 1026 and thenwritten to the solid state non-volatile memory. It will be appreciatedthat encoding may also be performed in parallel, for example, byproviding a number of TCMs 1024 operating in parallel, therebyincreasing the processing speed. Decoding of user data is performed byreversing the operations discussed in relation to FIG. 10B.

Depending on the encoding technique selected, one of several generatorpolynomials may be used. Merely by way of example, generator polynomialsas illustrated in Table 3 are used with systematic encoders with a rate½ code for some applications. The number of branches per state is equalto two.

TABLE 3 Generator Polynomials Order Polynomial 2 [1 D/D² + 1] 3 [1D²/D³ + D + 1] 4 [1 D²/D⁴ + D + 1] 5 [1 D²/D⁵ + D² + 1]

Set partitioning for Level 1 is:

-   -   Q(0)—{−15,−11,−7,−3,+1,+,5+9,+13}    -   Q(1)—{−13,−9,−5,−1,+3,+7,+11,+15}

Set partitioning for Level 2 is:

-   -   Q(00)—{−15,−7,+1,+9},    -   Q(10)—{−11,−3,+5,+13}    -   Q(01)—{−13,−5,+3,+11}    -   Q(11)—{−9,−1,+7,+15}

As illustrated in FIG. 10B, some embodiments of the present inventionutilize an RS encoder as outer encoder 1022. RS encoders provide afunctionality of being well suited for applications in which bursts oferrors are present. For solid state non-volatile memory applications,errors may occur in bursts for several reasons. First, defects in aportion of a memory array media may impact the error caused by the cellsdisposed in such portions. Additionally, error bursts may result fromoperation of the inner encoder 1024. A convolutional decoder may producebursts of errors since the output at any given time depends, in part, onprevious outputs. Thus, some embodiments of the present inventionutilize RS encoders and decoders suited for handling error bursts.

As seen from FIG. 1, the PDF of the programmed cells is differentdepending on the cell's threshold voltage. If the four levels are spacedequally, then the level corresponding to cells with a PDF defined by athreshold voltage ranging between 2 and 4 volts is more prone to errorsthan other levels due to its wider distribution. Accordingly, in someembodiments, constrained coding is used to inhibit certain patterns orreduce their frequency. For example, lowering the frequency of datacorresponding to cells with a PDF defined by a threshold voltage rangingbetween 2 and 4 volts lowers the overall error probability.

In some embodiments, the codeword size is aligned with the sector size.For example, if the sector size is, for example, 256 kbits, the innercode and outer code may be configured such that one outer codeword is256 kbits. Smaller or larger codeword sizes relative to the sector sizemay also be used. In FIG. 11A, the sector size is shown as being equalto the codeword size. In the case of smaller codeword size, each sectorincludes several codewords, as shown in FIG. 11B. In the case of largercodeword size, each codeword includes several sectors, as shown in FIG.11C. In general, the larger the codeword size, the larger the codinggain, the longer decoding delay, and the higher is the decodercomplexity.

Codewords may be interleaved before being stored. FIG. 12 shows anexemplary 3-way interleaved cell in which cells 1202 form codeword 1,cells 1204 form codeword 2, and cells 1206 form codeword 3. If a defectspans no more than three cells, it causes only one symbol error in eachcodeword, which is easier to correct than a burst of three symbolerrors.

In accordance with other exemplary embodiments of the present invention,coding of data, as described above may be applied across a multitude ofnon-volatile solid-state semiconductor memories, that in someembodiments are physically stacked on top of one another. For example,if 8 such non-volatile solid-state semiconductor memories are stackedtogether, a GF(2⁸)-based RS code may be applied across these memories,where each bit of a RS code symbol comes from one of these memories.Coding across such memories improves error recovery in the event one ofthese memories has large defects.

FIG. 13A is a simplified schematic diagram of an interleaving techniqueprovided according to an exemplary embodiment of the present invention.As illustrated in FIG. 13A, an inner encoder, for example, a TCMencoder, is utilized on rows of data and an outer encoder, for example,an RS encoder, is utilized on block columns of data. This exemplaryembodiment may be used, for example, in solid state non-volatilememories, in which the data is written to the memory cells in arectangular format, i.e., blocks. In situations in which a multi-biterror of significant length is present on the inner TCM code,embodiments of the present invention provide that several independentouter RS codes process data corrupted by the multi-bit error.Accordingly, the number of errors impacting an individual RS code islimited. Referring to FIG. 13A, the number of columns in a particularimplementation is determined, in part, by the maximum error burstlength. The number of rows is determined, in part, by the number ofsectors per block codeword.

According to some embodiments of the present invention, the number ofcolumns is predetermined depending on the particular application. Forexample, if the number of columns (related to the interleaving depth) islarger than the maximum error burst length, then the outer encoderoperating on the columns is similar to a memoryless channelcharacterized by a particular symbol error rate. Accordingly, errorbursts that occur affect different outer encoder codes. The symbol errorrate is typically determined by using TCM simulations independently, andthe error probability may be estimated by independent modeling. Thepercentage of overhead of the outer encoder, for example, an RS encoder,may be reduced by increasing the row dimension of the block codeword.Alternatively, one can increase the row dimension of the RS code whilekeeping the overhead percentage constant, thereby allowing for a highercorrection power per column.

FIG. 13B is a plot of SER as a function of SNR for an interleaved systemas illustrated in FIG. 13A. To compute the data presented in FIG. 13B,10 columns and 10 sectors per block codeword were utilized. Otherembodiments will utilize a varying number of columns and sectors perblock codeword depending on the particular application. The SER for anuncoded 2 bits/cell 4-PAM system is illustrated for purposes ofcomparison. The SER values for implementations in which the strength ofthe outer encoder (an RS encoder in this example) is varied over a rangeof correction powers are shown (t_(RS)=12, 14, and 16, respectively). Asthe correction power or strength of the outer encoding increases, theSNR at which the coded system drops to a level equal to the uncodedsystem decreases. Referring to FIG. 13B, this cross-over point is atapproximately 22.4 dB, 22.2 dB, and 22.0 dB for t_(RS)=12, 14, and 16,respectively.

In a particular exemplary embodiment, a multi-level solid statenon-volatile memory includes, for example, 2.5 bits/cell. In suchembodiments, two adjacent 8-level cells (3 bits/cell) form a 64-QAMmodulation symbol. Of the six bits in the 64-QAM modulation symbol, fivebits are utilized for data and one bit is used for encoding. Thus, insuch exemplary embodiments, the code rate is ⅚ and the number ofbranches per state is equal to four. Such a system provides 2.5bits/cell as 5 data bits are stored between two adjacent cells. In suchexemplary embodiments, the coding gain in comparison with an uncoded4-PAM system may be, for example, 0.423 dB for 16 states. It should benoted that calculation results will be modified as multiplicities areincluded in such calculations. For example, losses of approximately 0.2dB are expected with the doubling of multiplicities. One of ordinaryskill in the art would recognize many variations, modifications, andalternatives.

In another particular exemplary embodiment of the present invention,multi-level solid state non-volatile memory systems with, for example,3.5 bits/cell are provided. In such embodiments, two adjacent 16-levelcells (4 bits/cell) form a 256-QAM modulation symbol. Of the eight bitsin the 256-QAM modulation symbol, seven bits are utilized for data andone bit is used for encoding. Thus, in such exemplary embodiments thecode rate is ⅞ and the number of branches per state is equal to four.Such a system provides 3.5 bits/cell as 7 data bits are stored betweentwo adjacent cells. The coding gain in comparison with an uncoded 8-PAMsystem may be, for example, 0.527 dB for 8 states and 1.317 dB for 16states. It should be noted that calculation results will be modified asmultiplicities are included in such calculations. For example, losses ofapproximately 0.2 dB are expected with the doubling of multiplicities.One of ordinary skill in the art would recognize many variations,modifications, and alternatives.

Referring now to FIGS. 14A-14G, various exemplary implementations of thepresent invention are shown. Referring to FIG. 14A, the presentinvention may be embodied in a hard disk drive 1400. The presentinvention may implement either or both signal processing and/or controlcircuits, which are generally identified in FIG. 14A at 1402. In someimplementations, signal processing and/or control circuit 1402 and/orother circuits (not shown) in HDD 1400 may process data, perform codingand/or encryption, perform calculations, and/or format data that isoutput to and/or received from a magnetic storage medium 1406.

HDD 1400 may communicate with a host device (not shown) such as acomputer, mobile computing devices such as personal digital assistants,cellular phones, media or MP3 players and the like, and/or other devicesvia one or more wired or wireless communication links 1408. HDD 1400 maybe connected to memory 1409, such as random access memory (RAM), a lowlatency nonvolatile memory such as flash memory, read only memory (ROM)and/or other suitable electronic data storage.

Referring now to FIG. 14B, the present invention may be embodied in adigital versatile disc (DVD) drive 1410. The present invention mayimplement either or both signal processing and/or control circuits,which are generally identified in FIG. 14B at 1412, and/or mass datastorage 1418 of DVD drive 1410. Signal processing and/or control circuit1412 and/or other circuits (not shown) in DVD drive 1410 may processdata, perform coding and/or encryption, perform calculations, and/orformat data that is read from and/or data written to an optical storagemedium 1416. In some implementations, signal processing and/or controlcircuit 1412 and/or other circuits (not shown) in DVD drive 1410 canalso perform other functions such as encoding and/or decoding and/or anyother signal processing functions associated with a DVD drive.

DVD drive 1410 may communicate with an output device (not shown) such asa computer, television or other device via one or more wired or wirelesscommunication links 1417. DVD drive 1410 may communicate with mass datastorage 1418 that stores data in a nonvolatile manner. Mass data storage1418 may include a hard disk drive (HDD) such as that shown in FIG. 14A.The HDD may be a mini HDD that includes one or more platters having adiameter that is smaller than approximately 1.8″. DVD drive 1410 may beconnected to memory 1419, such as RAM, ROM, low latency nonvolatilememory such as flash memory, and/or other suitable electronic datastorage.

Referring now to FIG. 14C, the present invention may be embodied in ahigh definition television (HDTV) 1420. The present invention mayimplement either or both signal processing and/or control circuits,which are generally identified in FIG. 14C at 1422, a WLAN interfaceand/or mass data storage of the HDTV 1420. HDTV 1420 receives HDTV inputsignals in either a wired or wireless format and generates HDTV outputsignals for a display 1426. In some implementations, signal processingcircuit and/or control circuit 1422 and/or other circuits (not shown) ofHDTV 1420 may process data, perform coding and/or encryption, performcalculations, format data and/or perform any other type of HDTVprocessing that may be required.

HDTV 1420 may communicate with mass data storage 1427 that stores datain a nonvolatile manner such as optical and/or magnetic storage devices.At least one HDD may have the configuration shown in FIG. 14A and/or atleast one DVD drive may have the configuration shown in FIG. 14B. TheHDD may be a mini HDD that includes one or more platters having adiameter that is smaller than approximately 1.8″. HDTV 1420 may beconnected to memory 1428 such as RAM, ROM, low latency nonvolatilememory such as flash memory and/or other suitable electronic datastorage. HDTV 1420 also may support connections with a WLAN via a WLANnetwork interface 1429.

Referring now to FIG. 14D, the present invention may be embodied in acontrol system, a WLAN interface and/or mass data storage of a vehicle1030. In some implementations, the present invention implements apowertrain control system 1432 that receives inputs from one or moresensors such as temperature sensors, pressure sensors, rotationalsensors, airflow sensors and/or any other suitable sensors and/or thatgenerates one or more output control signals such as engine operatingparameters, transmission operating parameters, and/or other controlsignals.

The present invention may also be embodied in other control system 1440of vehicle 1430. Control system 1440 may likewise receive signals frominput sensors 1442 and/or output control signals to one or more outputdevices 1444. In some implementations, control system 1440 may be partof an anti-lock braking system (ABS), a navigation system, a telematicssystem, a vehicle telematics system, a lane departure system, anadaptive cruise control system, a vehicle entertainment system such as astereo, DVD, compact disc system and the like. Still otherimplementations are contemplated.

Powertrain control system 1432 may communicate with mass data storage1446 that stores data in a nonvolatile manner. Mass data storage 1446may include optical and/or magnetic storage devices for example HDDsand/or DVD drives. At least one HDD may have the configuration shown inFIG. 14A and/or at least one DVD drive may have the configuration shownin FIG. 14B. The HDD may be a mini HDD that includes one or moreplatters having a diameter that is smaller than approximately 1.8″.Powertrain control system 1432 may be connected to memory 1447 such asRAM, ROM, low latency nonvolatile memory such as flash memory and/orother suitable electronic data storage. Powertrain control system 1432also may support connections with a WLAN via a WLAN network interface1448. The control system 1440 may also include mass data storage, memoryand/or a WLAN interface (all not shown).

Referring now to FIG. 14E, the present invention may be embodied in acellular phone 1450 that may include a cellular antenna 1451. Thepresent invention may implement either or both signal processing and/orcontrol circuits, which are generally identified in FIG. 14E at 1452, aWLAN interface and/or mass data storage of the cellular phone 1450. Insome implementations, cellular phone 1450 includes a microphone 1456, anaudio output 1458 such as a speaker and/or audio output jack, a display1460 and/or an input device 1462 such as a keypad, pointing device,voice actuation and/or other input device. Signal processing and/orcontrol circuits 1452 and/or other circuits (not shown) in cellularphone 1450 may process data, perform coding and/or encryption, performcalculations, format data and/or perform other cellular phone functions.

Cellular phone 1450 may communicate with mass data storage 1464 thatstores data in a nonvolatile manner such as optical and/or magneticstorage devices for example HDDs and/or DVD drives. At least one HDD mayhave the configuration shown in FIG. 14A and/or at least one DVD drivemay have the configuration shown in FIG. 14B. The HDD may be a mini HDDthat includes one or more platters having a diameter that is smallerthan approximately 1.8″. Cellular phone 1450 may be connected to memory1466 such as RAM, ROM, low latency nonvolatile memory such as flashmemory and/or other suitable electronic data storage. Cellular phone1450 also may support connections with a WLAN via a WLAN networkinterface 1468.

Referring now to FIG. 14F, the present invention may be embodied in aset top box 1480. The present invention may implement either or bothsignal processing and/or control circuits, which are generallyidentified in FIG. 14F at 1484, a WLAN interface and/or mass datastorage of the set top box 1480. Set top box 1480 receives signals froma source such as a broadband source and outputs standard and/or highdefinition audio/video signals suitable for a display 1488 such as atelevision and/or monitor and/or other video and/or audio outputdevices. Signal processing and/or control circuits 1484 and/or othercircuits (not shown) of the set top box 1480 may process data, performcoding and/or encryption, perform calculations, format data and/orperform any other set top box function.

Set top box 1480 may communicate with mass data storage 1490 that storesdata in a nonvolatile manner. Mass data storage 1490 may include opticaland/or magnetic storage devices for example HDDs and/or DVD drives. Atleast one HDD may have the configuration shown in FIG. 14A and/or atleast one DVD drive may have the configuration shown in FIG. 14B. TheHDD may be a mini HDD that includes one or more platters having adiameter that is smaller than approximately 1.8″. Set top box 1480 maybe connected to memory 1494 such as RAM, ROM, low latency nonvolatilememory such as flash memory and/or other suitable electronic datastorage. Set top box 1480 also may support connections with a WLAN via aWLAN network interface 1496.

Referring now to FIG. 14G, the present invention may be embodied in amedia player 1472. The present invention may implement either or bothsignal processing and/or control circuits, which are generallyidentified in FIG. 14G at 1471, a WLAN interface and/or mass datastorage of the media player 1472. In some implementations, media player1472 includes a display 1476 and/or a user input 1477 such as a keypad,touchpad and the like. In some implementations, media player 1472 mayemploy a graphical user interface (GUI) that typically employs menus,drop down menus, icons and/or a point-and-click interface via display1476 and/or user input 1477. Media player 1472 further includes an audiooutput 1475 such as a speaker and/or audio output jack. Signalprocessing and/or control circuits 1471 and/or other circuits (notshown) of media player 1472 may process data, perform coding and/orencryption, perform calculations, format data and/or perform any othermedia player function.

Media player 1472 may communicate with mass data storage 1470 thatstores data such as compressed audio and/or video content in anonvolatile manner. In some implementations, the compressed audio filesinclude files that are compliant with MP3 format or other suitablecompressed audio and/or video formats. The mass data storage may includeoptical and/or magnetic storage devices for example HDDs and/or DVDdrives. At least one HDD may have the configuration shown in FIG. 14Aand/or at least one DVD drive may have the configuration shown in FIG.14B. The HDD may be a mini HDD that includes one or more platters havinga diameter that is smaller than approximately 1.8″. Media player 1472may be connected to memory 1473 such as RAM, ROM, low latencynonvolatile memory such as flash memory and/or other suitable electronicdata storage. Media player 1472 also may support connections with a WLANvia a WLAN network interface 1474.

Referring to FIG. 14H, the present invention may be embodied in a Voiceover Internet Protocol (VoIP) phone 1483 that may include an antenna1439. The present invention may implement either or both signalprocessing and/or control circuits, which are generally identified inFIG. 14H at 1482, a wireless interface and/or mass data storage of theVoIP phone 1483. In some implementations, VoIP phone 1483 includes, inpart, a microphone 1487, an audio output 1489 such as a speaker and/oraudio output jack, a display monitor 1491, an input device 1492 such asa keypad, pointing device, voice actuation and/or other input devices,and a Wireless Fidelity (Wi-Fi) communication module 1486. Signalprocessing and/or control circuits 1482 and/or other circuits (notshown) in VoIP phone 1483 may process data, perform coding and/orencryption, perform calculations, format data and/or perform other VoIPphone functions.

VoIP phone 1483 may communicate with mass data storage 1402 that storesdata in a nonvolatile manner such as optical and/or magnetic storagedevices, for example hard disk drives HDD and/or DVDs. At least one HDDmay have the configuration shown in FIG. 14A and/or at least one DVD mayhave the configuration shown in FIG. 14B. The HDD may be a mini HDD thatincludes one or more platters having a diameter that is smaller thanapproximately 1.8″. VoIP phone 1483 may be connected to memory 1485,which may be a RAM, ROM, low latency nonvolatile memory such as flashmemory and/or other suitable electronic data storage. VoIP phone 1483 isconfigured to establish communications link with a VoIP network (notshown) via Wi-Fi communication module 1486. Still other implementationsin addition to those described above are contemplated.

The above embodiments of the present invention are illustrative and notlimitative. Various alternatives and equivalents are possible. Theinvention is not limited by the type of comparator, counter, pulse-widthmodulator, driver, or filter used. The invention is not limited by thetype of amplifier used to establish the reference charging anddischarging currents. The invention is not limited by the of oscillator.The invention is not limited by the type of integrated circuit in whichthe present disclosure may be disposed. Nor is the invention limited toany specific type of process technology, e.g., CMOS, Bipolar, or BICMOSthat may be used to manufacture the present disclosure. Other additions,subtractions or modifications are obvious in view of the presentdisclosure and are intended to fall within the scope of the appendedclaims.

What is claimed is:
 1. A controller for a multi-level, solid-state,non-volatile memory having memory cells, the memory cells configured tostore data using a first number of digital levels, the controllercomprising: a first encoder configured to generate second data, inresponse to first data, for storage in the multi-level, solid-state,non-volatile memory, wherein voltages of the memory cells that areprogrammed to a first level of the digital levels are described by afirst probability density function having a first width, voltages of thememory cells that are programmed to a second level of the digital levelsare described by a second probability density function having a secondwidth, the first width is greater than the second width, and the firstencoder is configured to reduce a first frequency of the first level inthe second data compared to a second frequency of the second level inthe second data; and an analog-to-digital converter configured to, inresponse to one of the memory cells of the multi-level, solid-state,non-volatile memory, output a respective digital signal, wherein therespective digital signal is selected from a second number of digitallevels that is greater than the first number of digital levels.
 2. Thecontroller of claim 1, further comprising a first decoder configured todecode the respective digital signal to create decoded digital signals.3. The controller of claim 2, further comprising a second encoderconfigured to generate the first data in response to input data.
 4. Thecontroller of claim 3, further comprising a second decoder configured tofurther decode the decoded digital signals.
 5. The controller of claim3, wherein the first encoder includes a low-density parity-check encoderand wherein the second encoder includes a Reed-Solomon encoder.
 6. Thecontroller of claim 3, wherein the first encoder is configured toperform a first ECC technique and the second encoder is configured toperform a second ECC technique, wherein the first ECC technique isdifferent than the second ECC technique.
 7. The controller of claim 1,wherein the first encoder performs first encoding using softinformation.
 8. The controller of claim 1, wherein the first encoderincludes at least one of a trellis-coded modulation encoder, a binaryencoder, a convolutional encoder, a low-density parity-check encoder,and an iterative encoder.
 9. The controller of claim 1, wherein themulti-level, solid-state, non-volatile memory includes flash memory. 10.An integrated circuit comprising the controller of claim
 1. 11. A methodfor operating a multi-level, solid-state, non-volatile memory havingmemory cells, the memory cells configured to store data using a firstnumber of digital levels, the method comprising: generating second data,in response to first data, for storage in the multi-level, solid-state,non-volatile memory using a first encoder, wherein voltages of thememory cells that are programmed to a first level of the digital levelsare described by a first probability density function having a firstwidth, voltages of the memory cells that are programmed to a secondlevel of the digital levels are described by a second probabilitydensity function having a second width, and the first width is greaterthan the second width; reducing a first frequency of the first level inthe second data compared to a second frequency of the second level inthe second data; outputting a respective digital signal in response toone of the memory cells of the multi-level, solid-state, non-volatilememory; and selecting the respective digital signal from a second numberof digital levels that is greater than the first number of digitallevels.
 12. The method of claim 11, further comprising decoding therespective digital signal to create decoded digital signals using afirst decoder.
 13. The method of claim 12, further comprising generatingthe first data in response to input data using a second encoder.
 14. Themethod of claim 13, further comprising decoding the decoded digitalsignals using a second decoder.
 15. The method of claim 13, wherein thefirst encoder includes a low-density parity-check encoder and whereinthe second encoder includes a Reed-Solomon encoder.
 16. The method ofclaim 13, wherein the first encoder is configured to perform a first ECCtechnique and the second encoder is configured to perform a second ECCtechnique, wherein the first ECC technique is different than the secondECC technique.
 17. The method of claim 11, wherein the first encoderperforms first encoding using soft information.
 18. The method of claim11, wherein the first encoder includes at least one of a trellis-codedmodulation encoder, a binary encoder, a convolutional encoder, alow-density parity-check encoder, and an iterative encoder.
 19. Themethod of claim 11, wherein the multi-level, solid-state, non-volatilememory includes flash memory.